Full text: Mapping without the sun

a result, the process no longer describes a global birth-and-death 
but regional expansions and shrinkages of the sets under study 
namely the front, the seats and the scar of the spread. We draw 
from the model instructive simulations and a precise predictor of 
scars that actually occurred in the State of Selangor during the 
period 2000-2004. 
For the moment, fire daily predictions were not tested. This will 
be a future work to undertake. 
Figure 8: Cumulative number of hot spots from 2000 to 2004, 
during the periods April-June (a), July-September (b), and 
October-December (c). 
a) b) c) 
The authors would like to thank The Cilix Corp. for having al 
lowed them to use their maps of fuel combustion and spread rate. 
Abdullah, M.J., M.R. Ibrahim, and A.R. Abdul Rahim : The inci 
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Figure 9: a) cumulative number of hot spots from 2000 to 2004, 
during the period January to March, b) and c) two simulations 
based on the input set a) with two values of k in the ratio 1.5. 
Selangor area a(S) is equal to 79, 969 pixels, and in the simula 
tion of Figure9c, the average number of Poisson points over the 
set S of Selangor is 500. On the other hand, the sum of the fuel 
amount over S equals 304,130, in dimensionless units. There 
fore, by integrating Equation(20) over S, we find numerically 
J s 0{x)d(x) = 7 g°g 6g = k f fw{x)d(x) 
from which we draw 
79,969 k 
k = 1.64 x 10~ 3 
4.2 Fire spread simulations 
If Io stands for the input set, then each point x of Io is replaced 
by one of the discs of Figure7, according to the value r(x) of the 
spread rate map at point x, which results in 5(x). Then, the simu 
lated new seats I\ = /3(/o) are obtained by intersecting each S(x) 
by a realization J of Poisson points, as indicated in Relation(2), 
with intensity 6 = kf w , and by taking the union for all x of Io- 
Finally, each point y of the set of new seats I\ is replaced in turn 
by S(y), and the dilation X2 = S(I\), as given by Relation(3), 
consists in the union of the discs S(y). 
Figure 9b and c depict two propagation simulations <5(/i) when 
we take a winter input set Io (Figure 9a), and when we use the 
two maps r and / of Figure 2. The two simulations differ by 
their coefficients k, which are taken such that kb/ k c = 1.5. The 
values chosen for kb amplifies the phenomenon. One will notice 
that most of the small hot spots of Figure 9a do not develop fires. 
This paper proposes a new Random set model, the random spread. 
More than the classical spatial birth-and-death processes, random 
spread depends strongly on the heterogeneity of the space, which 
appears via two functions of intensity (9) and extension (6). As 
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